# Pietro Cataldi

**Pietro Antonio Cataldi** (15 April 1548, Bologna – 11 February 1626, Bologna) was an Italian mathematician. A citizen of Bologna, he taught mathematics and astronomy and also worked on military problems. His work included the development of continued fractions and a method for their representation. He was one of many mathematicians who attempted to prove Euclid's fifth postulate.

Cataldi discovered the sixth and seventh perfect numbers by 1588.^{[1]} His discovery of the 6th, that corresponding to p=17 in the formula M_{p}=2^{p}-1, exploded a many-times repeated number-theoretical myth that the perfect numbers had units digits that invariably alternated between 6 and 8. (Until Cataldi, 19 authors going back to Nicomachus are reported to have made the claim, with a few more repeating this afterward, according to L.E.Dickson's *History of the Theory of Numbers*). Cataldi's discovery of the 7th (for p=19) held the record for the largest known prime for almost two centuries, until Leonhard Euler discovered that 2^{31} - 1 was the eighth Mersenne prime.^{[1]} Although Cataldi incorrectly claimed that p=23, 29, 31 and 37 all also generate Mersenne primes (and perfect numbers), his text's clear demonstration shows that he had genuinely established primality through p=19.

### References

- ^
^{a}^{b}Caldwell, Chris.*The largest known prime by year*.

### External links

- O'Connor, John J.; Robertson, Edmund F., "Pietro Cataldi",
*MacTutor History of Mathematics archive*, University of St Andrews. - Galileo Project

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### Copyright

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